Diffusion of low-energy electrons in tissue-like liquids.

The spatial-energetic distribution of low-energy electrons was studied for a source located in a liquid medium simulating biological tissue. A time-independent Boltzmann equation was used to model this distribution microscopically. Ionization was treated as a perturbation to a quasi-elastic collision process between the electron and the medium. A diffusion limit was obtained by using a scale parameter, leading to a sequence of recursive partial differential equations whose solutions, associated with a macroscopic scale, were obtained by numerical approximations. As an application, electron ranges were estimated based on these solutions and then compared with values reported in the open literature based on experimental results and on Monte Carlo calculation. Local dosimetry, i.e., the energy imparted to a volume of a sphere with radius equal to the range of low-energy electrons, of low-energy electrons from internal emitters can benefit by the knowledge of the ranges estimated for biological tissue. Auger electron emitters, for example, have been the object of a number of investigations because of their radiobiological significance.

Calculation of water/air stopping-power ratios using EGS4 with explicit treatment of electron-positron differences.

Using the EGS4 Monte Carlo simulation program, a general purpose code has been written to calculate Bragg-Gray and Spencer-Attix stopping-power ratios for use in radiation dosimetry. The stopping-power ratios can be calculated in any material in any region in a general cylindrical geometry with a large number of source geometries possible. The calculations take into account for the first time the differences between the stopping powers and the inelastic scattering of positrons and electrons. The results show that previous calculations ignoring these effects were accurate. The present results agree, typically within 0.1%, with the Spencer-Attix water-to-air stopping-power ratios for broad parallel beams of electrons given in the AAPM and IAEA protocols except at the surface where the present calculations follow the buildup of secondary electrons in more detail and see a 2% reduction in the stopping-power ratios.